Mathematics · Discrete Mathematics
Graph Closeness Centrality Calculator
Calculate closeness centrality from reachable other-vertex count and sum of shortest-path distances.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=a/b with reachable other-vertex count=80 and sum of shortest-path distances=240.
- closeness centrality=0.3333333333333333.
Understand Graph Closeness Centrality
One idea, three depths
Choose how deeply to explain Graph Closeness Centrality
Graph Closeness Centrality: Calculate closeness centrality from reachable other-vertex count and sum of shortest-path distances.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Graph Closeness Centrality to answer this question: calculate closeness centrality from reachable other-vertex count and sum of shortest-path distances? Enter reachable other-vertex count and sum of shortest-path distances; the calculator shows closeness centrality. For example: reachable other-vertex count=80 and sum of shortest-path distances=240 produce closeness centrality=0.3333333333333333. The answer tells you closeness centrality.
Age 15Explain it to a 15-year-oldConnect it to the formula
A common closeness centrality divides reachable vertex count by the sum of shortest-path distances. This page evaluates the relationship directly. The rule is c=a/b. Its input values are reachable other-vertex count, sum of shortest-path distances, and the main result is closeness centrality. For example: reachable other-vertex count=80 and sum of shortest-path distances=240 produce closeness centrality=0.3333333333333333.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated graph closeness centrality relation over the valid real-number domain stated below. The implemented relation is c=a/b, evaluated from reachable other-vertex count, sum of shortest-path distances to produce closeness centrality. A common closeness centrality divides reachable vertex count by the sum of shortest-path distances. This page evaluates the relationship directly. Disconnected graphs require a harmonic or reachable-component convention.
Inputs and valid domain
- reachable other-vertex count must be a finite real number.
- sum of shortest-path distances must be a finite real number.
Important boundary: Disconnected graphs require a harmonic or reachable-component convention.
The formula
c=a/b
How the calculator works through it
It substitutes reachable other-vertex count, sum of shortest-path distances into the formula and exposes every numerical step above. The main output is closeness centrality.
Read the result correctly
The closeness centrality is the direct answer to “calculate closeness centrality from reachable other-vertex count and sum of shortest-path distances.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
reachable other-vertex count=80 and sum of shortest-path distances=240 produce closeness centrality=0.3333333333333333.
Where this model stops being reliable
Disconnected graphs require a harmonic or reachable-component convention.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Graph Closeness Centrality works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Graph Closeness Centrality uses c=a/b. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Sets, membership and finite collections
Sets provide the objects and membership rules that give Graph Closeness Centrality its discrete meaning.
Review this foundation about 6 min
Optional enrichment
- Ordered arrangements
Permutations connect Graph Closeness Centrality to systematic counting and arrangement problems.
Review this foundation about 5 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read reachable other-vertex count, sum of shortest-path distances.
- Evaluate the principal relationship: c=a/b.
- Return closeness centrality and check the domain conditions described above.
Python
from math import *
def graph_closeness_centrality_calculator(a, b) -> float:
return (a / b)
assert abs(graph_closeness_centrality_calculator(80, 240) - 0.3333333333333333) < 1e-6 * max(1.0, abs(0.3333333333333333))
C
#include <assert.h>
#include <math.h>
double graph_closeness_centrality_calculator(double a, double b) {
return (a / b);
}
int main(void) {
const double expected = 0.3333333333333333;
const double actual = graph_closeness_centrality_calculator(80, 240);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double graph_closeness_centrality_calculator(double a, double b) {
return (a / b);
}
int main() {
constexpr double expected = 0.3333333333333333;
const double actual = graph_closeness_centrality_calculator(80, 240);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double graph_closeness_centrality_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global graph_closeness_centrality_calculator
section .text
graph_closeness_centrality_calculator:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
divsd xmm0, [rbp-16]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = graph_closeness_centrality_calculator(a, b)
result = (a / b);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a / b);
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Graph Closeness Centrality Calculator. MW SysArc Tools. https://math.mwsysarc.com/discrete-mathematics/graph-closeness-centrality-calculator
MLA 9
MW SysArc. “Graph Closeness Centrality Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/discrete-mathematics/graph-closeness-centrality-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Graph Closeness Centrality Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/discrete-mathematics/graph-closeness-centrality-calculator.
Harvard
MW SysArc (2026) ‘Graph Closeness Centrality Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/discrete-mathematics/graph-closeness-centrality-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_graph_closeness_centrality_calculator_2026,
author = {{MW SysArc}},
title = {Graph Closeness Centrality Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/discrete-mathematics/graph-closeness-centrality-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Graph Closeness Centrality Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/discrete-mathematics/graph-closeness-centrality-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Graph Closeness Centrality do?
Calculate closeness centrality from reachable other-vertex count and sum of shortest-path distances.
How does the Graph Closeness Centrality work?
The calculator applies c=a/b. A common closeness centrality divides reachable vertex count by the sum of shortest-path distances. This page evaluates the relationship directly.
What can I learn from the Graph Closeness Centrality?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .